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Basic Arithmetic

The Building Blocks

Arithmetic is the foundation of math. It's all about working with numbers using a few core operations. The two most basic are addition and subtraction.

Addition is simply combining things. If you have 3 apples and you get 2 more, you add them together to find the total: $3 + 2 = 5$. Subtraction is the opposite; it’s taking things away. If you start with 5 apples and eat 2, you subtract to see what's left: $5 - 2 = 3$. These two operations are inverses of each other.

Next up are multiplication and division. Think of multiplication as a shortcut for repeated addition. Instead of writing 4+4+44 + 4 + 4, you can just write 3×43 \times 4. Both equal 12. It's a faster way to handle equal-sized groups.

Division is the inverse of multiplication. It’s the process of splitting a number into equal parts or seeing how many times one number fits into another. If you have 12 cookies to share among 3 friends, you divide: 12÷3=412 \div 3 = 4. Each friend gets 4 cookies.

Arithmetic

noun

The branch of mathematics dealing with the properties and manipulation of numbers through basic operations like addition, subtraction, multiplication, and division.

Putting It All Together

What happens when you have a problem with more than one operation, like 3+5×23 + 5 \times 2? If you work from left to right, you get 8×2=168 \times 2 = 16. But if you multiply first, you get 3+10=133 + 10 = 13. Different answers from the same problem! To avoid this confusion, mathematicians agreed on a standard order of operations.

This order is often remembered by the acronym PEMDAS.

LetterStands ForWhat to Do
PParenthesesAlways solve what's inside parentheses first.
EExponentsNext, handle any exponents (powers like 424^2).
MDMultiplication and DivisionThen, do all multiplication and division from left to right.
ASAddition and SubtractionFinally, do all addition and subtraction from left to right.

It's crucial to remember that multiplication and division have the same priority. The same goes for addition and subtraction. For these pairs, you just work from left to right.

Let's solve an example using PEMDAS: 10−2×(6−3)+42÷810 - 2 \times (6 - 3) + 4^2 \div 8.

10−2×(6−3)+42÷8Parentheses=10−2×3+42÷8Exponents=10−2×3+16÷8Multiplication (left to right)=10−6+16÷8Division (left to right)=10−6+2Subtraction (left to right)=4+2Addition (left to right)=6\begin{aligned} &10 - 2 \times \mathbf{(6 - 3)} + 4^2 \div 8 \\ &\quad \mathbf{P} \text{arentheses} \\ = &10 - 2 \times 3 + \mathbf{4^2} \div 8 \\ &\quad \mathbf{E} \text{xponents} \\ = &10 - \mathbf{2 \times 3} + 16 \div 8 \\ &\quad \mathbf{M} \text{ultiplication (left to right)} \\ = &10 - 6 + \mathbf{16 \div 8} \\ &\quad \mathbf{D} \text{ivision (left to right)} \\ = &\mathbf{10 - 6} + 2 \\ &\quad \mathbf{S} \text{ubtraction (left to right)} \\ = &\mathbf{4 + 2} \\ &\quad \mathbf{A} \text{ddition (left to right)} \\ = &6 \end{aligned}

Arithmetic in Real Life

These rules aren't just for math class. We use them all the time, often without even thinking about it. Every time you shop, budget, or cook, you're using arithmetic.

Lesson image

Imagine you're at a cafe. You buy a coffee for $3, a sandwich for $8, and a cookie for $2. To find your total bill, you add the costs together.

$3 + 8 + 2 = 13$

Your total is $13. If you pay with a $20 bill, how much change do you get back? That's a subtraction problem.

$20 - 13 = 7$

You get $7 back in change.

Now, let's say you and two friends decide to split that 💲13 bill evenly. This is where division comes in.

13÷3≈4.3313 \div 3 \approx 4.33

Each person should pay about 💲4.33.

These simple operations are the tools you use to make sense of the numbers all around you. Mastering them is the first and most important step to understanding the world of finance and beyond.

Quiz Questions 1/5

Which operation is considered a shortcut for repeated addition?

Quiz Questions 2/5

Addition and subtraction have the same priority in the order of operations and should be solved from left to right.